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arXiv:2003.06355 · Physical Review A

Photon and phonon spectral functions for continuum quantum optomechanics

Hashem Zoubi

Published Apr 3, 2020• 5 citations
arXivHTMLPDF

Abstract

We study many-particle phenomena of propagating multimode photons and phonons interacting through a Brillouin scattering type Hamiltonian in nanoscale waveguides. We derive photon and phonon retarded Green's functions and extract their spectral functions in applying the factorization approximation of the mean-field theory. The real part of the self-energy provides renormalization energy shifts for the photons and the phonons. Besides the conventional leaks, the imaginary part gives effective photon and phonon damping rates induced due to many-particle phenomena. The results extend the simple spectral functions of quantum optomechanics into continuum quantum optomechanics. We present the influence of thermal phonons on the photon effective damping rates and consider cases of specific photon fields to be excited within the waveguide and which are of importance for phonon cooling scenarios.

DOI
10.1103/physreva.101.043803

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In this paper we theoretically show that counterpart photonic Cooper pairs can be achieved in nanoscale waveguides with radiation pressure effect. We demonstrate that due to Brillouin scattering a Stokes photon and an anti-Stokes one can exchange virtual phonons, leading to an effective photon-photon interaction. The effective interaction Hamiltonian of the two photons is identical to that for electrons in the BCS theory, and the photonic counterpart of the superconducting energy gap can appear. Quite different from the conventional stimulated Brillouin scattering the number of photon pairs can be amplified. The result could be used as a photon-pair laser and might have a possible application in integrated optics and quantum information processing in the future.
We develop a systematic method for deriving a quantum optical multi-mode Hamiltonian for the interaction of photons and phonons in nanophotonic dielectric materials by applying perturbation theory to the electromagnetic Hamiltonian. The Hamiltonian covers radiation pressure and electrostrictive interactions on equal footing. As a paradigmatic example, we apply our method to a cylindrical nanoscale waveguide. We use the resulting multi-mode Hamiltonian to derive an effective phonon-mediated interaction between photons propagating in the material. We predict strong non-linear phase shifts even among two photons, comparable to what can be achieved in nonlinear atomic media (comprising cold Rydberg atoms).
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